Taking fear back into the Marginal Value Theorem: the risk-MVT and optimal boldness

Abstract

AbstractForagers exploiting heterogeneous habitats must make strategic movement decisions in order to maximize fitness. Foraging theory has produced very general and insightful formalizations of the optimal patch-leaving decisions rational individuals should make. One is the Marginal Value Theorem (MVT), which models the sequential visit of habitat patches and their spatial distribution, as encapsulated in the travel time, i.e. the average time it takes to move from one patch to another. The MVT has a simple intuitive graphical interpretation in terms of gain functions and travel times. However, it considers only energy gains, and the effect of predation risk on the time allocation strategy is notoriously lacking. An important development that includes predation risk was Brown’s (1988) economic treatment of optimal patch leaving decisions, often cited as an extension of the MVT, and forming the basis of GUD theory. However, it is a more abstract result that does not have the specificities or graphical appeal of the MVT. Although both successful, the two theories are seldom connected; textbook presentations of the MVT typically do not cover Brown’s developments, and reciprocally. Here we formally introduce the risk-MVT (rMVT), showing how the systematic introduction of the different possible types of risk into the original MVT yields generalized rMVT equations. Much of the graphical simplicity of the MVT is retained, provided one uses the appropriate risk-relative timescale, such as the micromort units used in decision analysis. Optimal strategies under the risk-MVT can be used to define the “optimal boldness” in a habitat. We show that Brown’s GUD-theory is equivalent to a rMVT, but only for one particular possible definition of fitness. Reconciling the two theories could help behavioral ecologists take the best of two worlds.